Answer:
a straight line through the zero
If 75% = 108 then
100% = 81
Answer:
C) ![x^{2} + y^{2} - 12x + 2y + 21 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20%20y%5E%7B2%7D%20-%2012x%20%2B%202y%20%2B%2021%20%3D%200)
Equation of a circle:
![(x-a)^{2} +(y-b)^{2} =r^{2}](https://tex.z-dn.net/?f=%28x-a%29%5E%7B2%7D%20%2B%28y-b%29%5E%7B2%7D%20%3Dr%5E%7B2%7D)
Substitute into the equation
a = 6
b = -1
r = 4
![(x-6)^{2} +(y--1)^{2} =4^{2}](https://tex.z-dn.net/?f=%28x-6%29%5E%7B2%7D%20%2B%28y--1%29%5E%7B2%7D%20%3D4%5E%7B2%7D)
![(x-6)^{2} +(y+1)^{2} =16](https://tex.z-dn.net/?f=%28x-6%29%5E%7B2%7D%20%2B%28y%2B1%29%5E%7B2%7D%20%3D16)
Expand and Simplify
![(x-6)^{2} = x^{2} - 12x + 36](https://tex.z-dn.net/?f=%28x-6%29%5E%7B2%7D%20%3D%20x%5E%7B2%7D%20-%2012x%20%2B%2036)
![(y+1)^{2} = y^{2} + 2y + 1](https://tex.z-dn.net/?f=%28y%2B1%29%5E%7B2%7D%20%3D%20y%5E%7B2%7D%20%2B%202y%20%2B%201)
![x^{2} - 12x + 36 + y^{2} + 2y + 1 = 16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-%2012x%20%2B%2036%20%2B%20y%5E%7B2%7D%20%2B%202y%20%2B%201%20%3D%2016)
![x^{2} + y^{2} - 12x + 2y + 36 + 1 = 16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20y%5E%7B2%7D%20-%2012x%20%2B%202y%20%2B%2036%20%2B%20%201%20%3D%2016)
![x^{2} + y^{2} - 12x + 2y + 36 + 1 - 16 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20y%5E%7B2%7D%20-%2012x%20%2B%202y%20%2B%2036%20%2B%20%201%20-%2016%20%3D%200)
![x^{2} + y^{2} - 12x + 2y + 21 = 0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20y%5E%7B2%7D%20-%2012x%20%2B%202y%20%2B%2021%20%3D%200)
Given that the population has been modeled by the formula:
a=118e^(0.024t), the time taken for the population to hit 140k will be given by:
140000=118e^(0.024t)
solving for t we shall have:
140000/118=e^(0.024t)
thus;
0.024t=ln(140000/118)
t=1/0.024*ln(140000/118)
t=295
thus the time the population will be 140000 will be:
1998+295
=2293